Lallana has been linked with £25m Anfield move since the end of the season, while right-back Clyne – valued at £15m by Saints – is seen by as a potential replacement for Glen Johnson.
Spurs are being linked with a move for Real Madrid manager Carlo Ancelotti.
According to the Sunday Telegraph, the north London club will make one final check to see if the 54-year-old is interested in a move back to the Premier League.
If they draw a blank with Ancelotti, who guided the La Liga giants to Champions League glory last night, Spurs are expected to make a move for Saints boss Mauricio Pochettino.
England manager Roy Hodgson has banished agents from the team’s training camps in an attempt to avoid distractions over transfers affecting the mood of the squad. Full story: The Observer Juan Mata could be sold by Manchester United after less than a season with the club.
Team manager Louis van Gaal is ready to sell the midfielder to Barcelona for £40m, according to the Sunday Express. Mata signed for Manchester United from Chelsea in January for £37.1m.